Cryptographic Pairings Based on Elliptic Nets

Ogura, Naoki; Kanayama, Naoki; Uchiyama, Shigenori; Okamoto, Eiji

doi:10.1007/978-3-642-25141-2_5

Cited by 10 publications

(8 citation statements)

References 15 publications

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“…Ogura et al [7] gave explicit formulae based on elliptic nets for computing some variants of the Tate pairing, which contained the optimal ate pairing. We use the following:…”

Section: The Optimal Ate Pairing Via Elliptic Netsmentioning

confidence: 99%

“…2. ) This extension of the block allows us to compute Double or DoubleAdd without the recurrences (6) and (7). Although this technique increases the total cost, the cost of the critical path is reduced to the following three operations; one multiplication in F p 12 , one multiplication of the elements in F p 12 and F p 2 , and one addition in F p 12 .…”

Section: Outline Of Our Parallelizationmentioning

confidence: 99%

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The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

et al. 2016

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“…Ogura et al [7] gave explicit formulae based on elliptic nets for computing some variants of the Tate pairing, which contained the optimal ate pairing. We use the following:…”

Section: The Optimal Ate Pairing Via Elliptic Netsmentioning

confidence: 99%

Section: Outline Of Our Parallelizationmentioning

confidence: 99%

The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

et al. 2016

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“…Ogura et al [11] provided formulas for using elliptic nets to find cryptographic pairings. In this paper, we review only the formula for the Ate pairing.…”

Section: Using An Elliptic Net To Find An Ate Pairingmentioning

confidence: 99%

“…In 2007, Stange [10] defined elliptic nets and proposed an alternative method based on elliptic nets for computing Tate pairings. Ogura et al [11] presented formulas that use elliptic nets to compute cryptographic pairings.…”

Section: Introductionmentioning

confidence: 99%

Computing fixed argument pairings with the elliptic net algorithm

Liu

Kanayama

Saito³

et al. 2014

JSIAM Letters

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The pairing-based cryptosystem was proposed in 2001, and it provides efficient implementations of identity-based encryption (IBE) and attribute-based encryption (ABE). In 2010, Costello and Stebila introduced the concept of fixed argument pairing, which can be applied to many applications of pairings, and, to compute these pairings, they proposed an efficient algorithm based on the Miller algorithm. In this paper, we propose a method for computing fixed argument pairings, based on the elliptic net method proposed by Stange.

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“…During her talk at Microsoft Research on January 30, 2007, she has described the various applications of elliptic nets in cryptography [10]. Since then, the higher-ranked elliptic nets on Weierstrass curves have been applied in the computation of Tate and r − Ate pairings [6]. Years later, the same theory of elliptic nets which employed polynomials has been applied in the calculation of scalar multiplications [2,5,12]; this is the primary goal and interest in this current paper.…”

Section: Introductionmentioning

confidence: 99%

Constructing Scalar Multiplication via Elliptic Net of Rank Two

Muslim¹,

Said²

2018

IJET

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Elliptic nets are a powerful method for computing cryptographic pairings. The theory of rank one nets relies on the sequences of elliptic divisibility, sets of division polynomials, arithmetic upon Weierstrass curves, as well as double and double-add properties. However, the usage of rank two elliptic nets for computing scalar multiplications in Koblitz curves have yet to be reported. Hence, this study entailed investigations into the generation of point additions and duplication of elliptic net scalar multiplications from two given points on the Koblitz curve. Evidently, the new net had restricted initial values and different arithmetic properties. As such, these findings were a starting point for the generation of higher-ranked elliptic net scalar multiplications with curve transformations. Furthermore, using three distinct points on the Koblitz curves, similar methods can be applied on these curves.

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Cryptographic Pairings Based on Elliptic Nets

Cited by 10 publications

References 15 publications

The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

Computing fixed argument pairings with the elliptic net algorithm

Constructing Scalar Multiplication via Elliptic Net of Rank Two

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